Open AccessNumerical solution to elliptic inverse problem with Neumann-type integral condition and overdetermination
Author(s) -
Charyyar Ashyralyyev,
A Cay
Publication year - 2020
Publication title -
ķaraġandy universitetìnìn̦ habaršysy. matematika seriâsy
Language(s) - English
Resource type - Journals
eISSN - 2663-5011
pISSN - 2518-7929
DOI - 10.31489/2020m3/5-17
Subject(s) - overdetermined system , mathematics , boundary value problem , mathematical analysis , inverse problem , partial differential equation , elliptic boundary value problem , elliptic curve , stability (learning theory) , von neumann stability analysis , elliptic operator , neumann boundary condition , free boundary problem , computer science , machine learning
In modeling various real processes, an important role is played by methods of solution source identification problem for partial differential equation. The current paper is devoted to approximate of elliptic over determined problem with integral condition for derivatives. In the beginning, inverse problem is reduced to some auxiliary nonlocal boundary value problem with integral boundary condition for derivatives. The parameter of equation is defined after solving that auxiliary nonlocal problem. The second order of accuracy difference scheme for approximately solving abstract elliptic overdetermined problem is proposed. By using operator approach existence of solution difference problem is proved. For solution of constructed difference scheme stability and coercive stability estimates are established. Later, obtained abstract results are applied to get stability estimates for solution Neumann-type overdetermined elliptic multidimensional difference problems with integral conditions. Finally, by using MATLAB program, we present numerical results for two dimensional and three dimensional test examples with short explanation on realization on computer.